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XV. Experiments relative to the effect of temperature on the refractive index and 
dispersive power of expansible fluids, and on the influence of these changes in a 
telescope with a fluid lens. By Peter Barlow, Esq. F.R.S. 8$c. 

Read May 15, 1828. 

AN a paper I had the honour to present to the Royal Society in January last, 
relative to the construction of achromatic telescopes with fluid lenses, I have 
stated that between the temperatures of 31° and 84° I had not been able to 
detect any very sensible change in the index denoting the focal length of the 
telescope : these observations however being made at intervals of some months, 
I was doubtful whether there might not be some minute variation which had 
escaped my notice ; and I have since, by means of temperature artificially pro- 
duced, ascertained that there is a certain small change, and the amount of that 
change, which is T V 5 o 4 oths of an inch in the length of the telescope employed, 
between each of these extremes and the mean temperature of 57°. That is, the 
eye-piece of the telescope and the fluid lens being fixed, as was the case in 
this instrument, the plate lens required an adjustment of 0.134 of an inch, 
between the temperature of 57° and each of the above extremes, to produce 
the brightest and most perfect image. 

Before I proceed, however, to detail the results of my inquiry on these sub- 
jects, it will be proper to define a few terms which appear in one or two in- 
stances to have been misunderstood. 

1. The length or focal length of the telescope, is the distance from the front 
lens to the focus. 

2. The fluid focus or fluid focal length, is the distance from the fluid lens 
to the focus. 

3. The focal power of the telescope, or the equivalent focal length, is the 
focal length of a telescope of the usual construction, which gives the same 
convergency to the rays or the same sized image as the telescope in question. 

mdcccxxviii. 2 s 



314 MR. BARLOW ON THE OPTICAL PROPERTIES OF EXPANSIBLE FLUIDS. 

In what follows : 

/ will denote the length of the telescope, 
/the focal length of the plate lens. 
/' the focal length of the fluid lens. 
/" the fluid focal length. 
/'" the equivalent focal length. 
d the distance of the lenses. 
Under the particular form of construction to which we are now referring, 
f and f" remain fixed or constant, but the rest are variable under different 
temperatures, in consequence of the effect which temperature produces in the 
value off. 

If we knew the change in the value of/"', or in the refractive index of the 
fluid under different temperatures, we might proceed immediately to compute 
its effects on the focal power of the telescope ; but as this may be considered 
doubtful, I have endeavoured to determine the effect on the power of the 
telescope by direct observations, and have thence computed the corresponding 
change in the refractive index of the fluid. 

In order to determine the change in the position of the front lens due to a 
certain range of the thermometer, I placed the telescope in a small room about 
twelve feet square in my garden, and having adjusted it very carefully to a 
dial-plate of a watch, at the distance of 150 feet, when the thermometer was 
at 40°, I had a fire lighted, the room shut up, and the temperature gradually 
raised to 75°, re-adjusting and registering the focus for every change of 5°. 

As, however, the intermediate changes were very small, it will be sufficient to 
state, that between the two extremes, viz. 40° and 75°, the whole change was 
0.177 of an inch ; and hence, supposing the change uniform for equal variations 
of temperature, we find for the difference between the mean temperature of 57° 
and each extreme before mentioned, viz. 31° and 84°, an alteration in the 
length of the telescope of .134 of an inch, as stated in the beginning of this 
paper. 

In the instrument on which these observations were made, the following are 
the values of the different quantities at the mean temperature 57°; viz./= 32.5, 

./' = 32.65, /" = 40.5, I = 54.92, d — 14.42, /'" — ¥r d — 72.8. 



MR. BARLOW ON THE OPTICAL PROPERTIES OF EXPANSIBLE FLUIDS. 315 

And since by the observations above referred to, the value of d varied 0.134 
of an inch between the mean temperature and each of the extremes, we have 
in one case d= \A.hhA, and in the other rf= 14.286. Whence the focal power 
of the telescope was 

at 31°, /'" = j£j - 73.34 

at 84°, /'" = &^ = 72.28 

So that the instrument being adjusted at the mean temperature 57°, and 

fitted with a micrometer, it will require a correction of about y^o oth part of the 

angular measure for every change of 1° in the thermometer • that is, a 60th 

part of a second for every minute in the angle, a quantity too small to require 

any notice, except in cases of extreme delicacy. 

In order to find the actual change in the focus of the fluid lens which 

rendered the foregoing adjustments of the plate lens necessary, we have 

_1 _1_ JL_ 1 1 ____ J_ 

f-d ~ f ~ f" ° r f-d ~ f» — f< ' 

In this expression, / ' = 40.5,/— (?at 31° = 17.946 

/— rfat57° = 18.080 
f—d at 84° = 18.214 
And substituting these values successively for f—d in the above expression, 
we find /' at 31° = 32.222 

/'at 57° = 32.650 
/' at 84° = 33.090 
And since it has been shown, Phil. Transrl827, Art. XV. that -Jjjj- — di- 
spersive ratio, We have at 31° dispersion = .3067 

57° dispersion = .3075 
84° dispersion = .3084 
a difference sufficiently small to baffle the most acute and experienced eye. 
The change therefore in the power and colour of the telescope is so small, and 
the correction due to it (in any case where such correction is thought necessary) 
so easily made, that an instrument on this construction may I trust be con- 
sidered just as applicable to all the nice purposes of modern astronomy, as one 
of the usual refractors of the same power. 

2 s 2 



316 MR. BARLOW ON THE OPTICAL PROPERTIES OF EXPANSIBLE FLUIDS. 

The very inconsiderable change in the focal power of the telescope led me 
to conclude, in the early part of my experiments, that no optical change took 
place in the fluid between the above limits, or at least that the change was 
extremely small. It appears however from the preceding experiments and 
investigation, that the permanency of the telescopic effect is attributable to 
the peculiar construction of the instrument, and that the change in the 
refractive index of the fluid is much more considerable than I had imagined ; 
for we have seen that the focal length of the fluid lens was at 31° = 32.22 

at 57° = 32.65 
at 84° = 33.03 
And since the focal length is cseteris paribus inversely as the index, and the 
index at 57° being 0.634, we find 32.22 : 32.65 : : 0.634 : 0.642 

33.09 : 32.65 : : 0.634 : 0.626 
Hence the mean index of the sulphuret of carbon is at 31° = 0.642 

at 57° = 0.634 
at 84° = 0.625 

That is, with a variation of temperature of 53° ; the change of index amounts 

017 
to ' 6g . = ^Vth part nearly of the whole index at 57°. 

Which, supposing the change to be uniformly proportional in greater ther- 
mometrical ranges, gives a change in the refractive index of nearly xoth 
between 32° and 212°. Now it has been stated on the result of experiment 
(Dr. Ure's Chemical Dictionary), that the expansion of sulphuret of carbon 
amounts to -j-th between the above limits. We have therefore strong reasons to 
conclude that in this, and all other expansible fluids, the index of refraction 
varies directly as the density ; the trifling difference in the two results being 
attributable, in all probability, to slight errors of observation in one or other 
of the two processes, so different from each other, from which these results are 
deduced. 

With respect to the dispersive ratio, it is probably the same at all tempe- 
ratures ; for, supposing 1 : 1 + a 1 : 1 + d, 1 : 1 -f a" to be the ratio of the 
sines of incidence and refraction of the extreme and mean rays of the spectrum 
at any given temperature, the dispersive power is expressed by ~f . And 
as we have seen that the mean index a' varies as the density of the fluid, we 



MR. BARLOW ON THE OPTICAL PROPERTIES OF EXPANSIBLE FLUIDS. 317 

have strong reason to suppose that a and a" vary also in the same proportion ; 
and if so, the dispersive power will of course remain constant ; and this de- 
duction is verified, as far as the, eye can judge of colour in the telescope, by the 
preceding experiments, which certainly indicated no perceptible change in the 
colour of the image. This, however, is a subject I intend to examine more 
particularly when my large telescope is completed. 

It may be proper to observe, that the form of the instrument here employed 
differs a little from that described in my former paper : in the latter, the plate 
lens is a fixture, and the adjustment is made by a slight motion of the fluid 
lens. In this I can move either lens at pleasure ; and I have chosen to fix the 
fluid, and to adjust the plate lens, merely for the sake of simplifying the 
investigation.